Problem: Solve for $k$, $ \dfrac{3k + 4}{2k - 10} = \dfrac{1}{7} $
Multiply both sides of the equation by $2k - 10$ $ 3k + 4 = \dfrac{2k - 10}{7} $ Multiply both sides of the equation by $7$ $ 7(3k + 4) = 2k - 10 $ $21k + 28 = 2k - 10$ $19k + 28 = -10$ $19k = -38$ $k = -\dfrac{38}{19}$ Simplify. $k = -2$